Review for NeurIPS paper: Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation: Bayesian inference for latent Gaussian models and beyond

This paper develops an inference method for Gaussian latent variable models that employs a Laplace approximation marginalize over latent variables and infer hyperparameters using HMC. The authors use an adjoint method to efficiently compute the gradient with respect to the hyperparameters. The main contribution is that inference can scale to hyperparameters that have a high dimensionality ( 1000). This paper was overall well-received by reviewers, who remained on balance in favor of acceptance after the author response. The main outstanding points of criticism, which the AC would like to encourage the authors to address are that: (1) the authors should more clearly motivate the use case for latent Gaussian models with a large number of parameters (2) discussion of recent advances in variational inference for GPs is warranted (and some form of comparison would be appreciated).